Various three-dimensional manipulatable toys and puzzles are known. A popular device which has sold under the trademark "Rubik's Cube" is a puzzle cube, each of whose six faces appears to be a 3.times.3 array of subcubes. The elements comprising each face can rotate about an axis perpendicular to that face. By a sequence of rotations of the various faces, individual elements can be moved from one face to another face of the main puzzle cube. In this manner, the puzzle can be manipulated into some predetermined arrangement of the subcubes, specified for example by the colors on the faces of the subcubes. However, in the Rubik puzzle, the center subcube of each face is attached to the axis of rotation for that face, preventing movement of the center subcube to another face. Indeed, the six axes of rotation intersect at the center of the main cube, and, together with each face's center subcube element, form a central framework about which all other puzzle elements rotate. This method of constructing a manipulatable puzzle limits the types of arrangements that can be achieved.
A number of variations and generalizations of the Rubik puzzle have been described. U.S. Pat. No. 4,432,548 describes a cubic block puzzle, related to the Rubik puzzle, wherein the center subcube of each face can be moved to other faces. This puzzle is constructed with a central cage about which the individual puzzle elements can move. Although the cage construction permits more general manipulation of the puzzle elements, the puzzle is still limited to a cubic array of elements, moving about a central framework.
Other puzzles are configured in 4.times.4.times.4 arrays (e.g., as described in U.S. Pat. Nos. 4,421,311 and 4,511,144) or 2.times.2.times.2 arrays (e.g., as described in U.S. Pat. Nos. 3,655,201 and 4,405,131), but all of these puzzles are also constructed with a central framework of some type. Still other three-dimensional puzzles are not restricted to cubic appearances (e.g., as described in U.S. Pat. Nos. 3,081,089, 4,344,623, 4,461,480, 4,473,228, and 4,478,418), but nevertheless are constructed with a central structure about which the puzzle elements move.
The presence of a central framework or structure in all of the previously-known puzzles not only limits the types of arrangements which can be achieved with a given puzzle, but also limits the overall appearance of the puzzle to closed, three-dimensional solids or lattice structures such as the central framework permits.